A variance-estimation-based stopping rule for symbolic dynamic filtering

Abstract

As an alternative to the batch means (BM) method in the stopping rule for symbolic dynamic filtering, this short paper presents an analytical procedure to estimate the variance parameter and to obtain a lower bound on the length of symbol blocks for constructing probabilistic finite state automata (PFSA). If the modulus of the second largest eigenvalue of the PFSA’s state transition matrix is relatively small or if the symbol block length is not too large, then the performance of the proposed stopping rule is superior to that of the stopping rule based on BM method. The algorithm of the proposed stopping rule is validated on ultrasonic data collected from a fatigue test apparatus for damage detection in the polycrystalline alloy 7075-T6.